Kalashnikov, Vyacheslav V.; Kalashnikova, Natalia I. Solving two-level variational inequality. (English) Zbl 0859.90114 J. Glob. Optim. 8, No. 3, 289-294 (1996). Summary: An approach to solving a mathematical program with variational inequality or nonlinear complementarity constraints is presented. It consists in a variational re-formulation of the optimization criterion and looking for a solution of thus obtained variational inequality among the points satisfying the initial variational constraints. Cited in 19 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49J40 Variational inequalities 93A13 Hierarchical systems 49M30 Other numerical methods in calculus of variations (MSC2010) Keywords:parametrization; pseudo-monotone mapping; penalty function algorithm; variational inequality; nonlinear complementarity constraints PDFBibTeX XMLCite \textit{V. V. Kalashnikov} and \textit{N. I. Kalashnikova}, J. Glob. Optim. 8, No. 3, 289--294 (1996; Zbl 0859.90114) Full Text: DOI References: [1] Harker, P.T., Choi, S.-C., ?A penalty function approach for mathematical programs with variational inequality constraints,? Information and Decision Technologies, 17 (1991), pp. 41-50. · Zbl 0732.90075 [2] Smith, M.J., ?A descent algorithm for solving monotone variational inequalities and monotone complementarity problems,? Journal of Optimization Theory and Applications, 44 (1984), pp. 485-496. · Zbl 0535.49023 · doi:10.1007/BF00935463 [3] Outrata, J.V., ?On optimization problems with variational inequality constraints?, SIAM Journal on Optimization, 4 (1994), pp. 340-357. · Zbl 0826.90114 · doi:10.1137/0804019 [4] Karamardian, S., ?An existence theorem for the complementarity problem,? Journal of Optimization Theory and Applications, 18 (1976), pp. 445-454. · Zbl 0304.49026 · doi:10.1007/BF00932654 [5] Eaves, B.C., ?On the basic theorem of complementarity,? Mathematical Programming, 1 (1971), pp. 68-75. · Zbl 0227.90044 · doi:10.1007/BF01584073 [6] Rockafellar, R.T., ?Convex Analysis,? Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401 [7] Harker, P.T., Pang, J.-S., ?Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications,? Mathematical Programming, 48 (1990), pp. 161-220. · Zbl 0734.90098 · doi:10.1007/BF01582255 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.